Teoremas fundamentales del cálculo

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=3 height=98 BGCOLOR="#006600" TEXT="#F7F7FF" bgproperties="fixed" background="05700732dwnpjk.jpg"> <div> <FONT SIZE="6" COLOR="#FFFFFF" FACE="Times New Roman" ><B>C á l c u l o   2 1</B></FONT><FONT SIZE="6" COLOR="#FFCC66" FACE="Arial" ><B> </B></FONT><FONT SIZE="2" COLOR="#FFFFCC" FACE="Arial" >   </FONT><B>  |   </B><A HREF="index.htm" TARGET="_top" TITLE="A n á l i s i s M a t e m á t i c o"><U><B>Home</B></U></A><B> |  </B><A HREF="id98.htm" TARGET="_top" TITLE=" | Contenido |"><U><B>Contenido</B></U></A><B> |  </B><A HREF="id341.htm" TARGET="_top" TITLE="Introducción al cálculo integral"><U><B>Cálculo integral</B></U></A><B> |</B></div> <div> <A HREF="id342.htm" TARGET="_top" TITLE="Área"><U>Área</U></A>   |   <A HREF="id344.htm" TARGET="_top" TITLE="La integral definida"><U>La integral definida</U></A>   |   <A HREF="id345.htm" TARGET="_top" 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</tr><tr> <td valign="top" rowspan="2" width=245 BGCOLOR="#006600" TEXT="#F7F7FF"> <div> <A HREF="id347_m.htm#primer_teorema_fundamental_del_c_lculo" TARGET="TRLX_Middle" TITLE="Teoremas fundamentales del cálculo"><U><B><IMG BORDER="0" SRC="Wing0a73007700c800660000.gif" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Primer teorema fundamental del cálculo</B></U></A></div> <div> <A HREF="id347_m.htm#segundo_teorema_fundamental_del_c_lculo" TARGET="TRLX_Middle" TITLE="Teoremas fundamentales del cálculo"><U><B><IMG BORDER="0" SRC="Wing0a73007700c800660000.gif" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Segundo teorema fundamental del cálculo</B></U></A></div> <div> <B><IMG BORDER="0" SRC="Wing0a73007700c800660000.gif" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Integración directa</B></div> <div> <B><IMG BORDER="0" SRC="Wing0a73007700c800660000.gif" HEIGHT="13" WIDTH="24" ALIGN="bottom" HSPACE="0" VSPACE="0">Integración por sustitución</B></div> </td> <td valign="top" height=361 colspan=2 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <U>Teoremas fundamentales del cálculo</U></div> <div>  <A NAME="primer_teorema_fundamental_del_c_lculo"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Primer teorema fundamental del cálculo:</B></FONT></div> <div> <IMG SRC="1648727c0.gif" border=0 width="626" height="124" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <div>  <A NAME="segundo_teorema_fundamental_del_c_lculo"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Segundo teorema fundamental del cálculo:</B></FONT></div> <div> <IMG SRC="1649724f0.gif" border=0 width="626" height="79" ALT="Documento Microsoft Office Word" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <bR> <DIV ALIGN="LEFT"></DIV> <div> <TABLE BORDER="1" CELLPADDING="1" CELLSPACING="1" WIDTH="606" BORDERCOLORLIGHT="#33FFCC" BORDERCOLORDARK="#009900" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 541 WIDTH="598"><div>  <A NAME="ejercicios_resueltos"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="1" ALIGN="bottom" WIDTH="1" HSPACE="0" VSPACE="0" ></A><FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" ><B>Ejercicios resueltos</B></FONT></div> <bR> <div> <FONT SIZE="3" COLOR="#0099FF" FACE="Times New Roman" ><B>E</B></FONT>n los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >1</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >14</FONT>, evalúe la integral definida. </div> <div> En los ejercicios <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >15</FONT> a <FONT SIZE="3" COLOR="#CC0033" FACE="Times New Roman" >21</FONT>, calcule la derivada. </div> <div> <FONT SIZE="3" COLOR="#00CC00" FACE="Times New Roman" ><B>Nota:</B></FONT> para resolver los ejercicios es necesario conocer algunas técnicas de integración, por el momento sólo es indispensable aprender la integración directa y la integración por sustitución.</div> <bR> <div> <A HREF="#1" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164a8c270.gif" border=0 width="140" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                     <A HREF="#2" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164b77270.gif" border=0 width="119" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                   <A HREF="#3" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164c71290.gif" border=0 width="113" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#4" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164d77270.gif" border=0 width="119" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                          <A HREF="#5" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164e69270.gif" border=0 width="105" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                       <A HREF="#6" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="164f84270.gif" border=0 width="132" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A> </div> <div> <A HREF="#7" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="16505f2b0.gif" border=0 width="95" height="43" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                                <A HREF="#8" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="16516b270.gif" border=0 width="107" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                      <A HREF="#9" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165285300.gif" border=0 width="133" height="48" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#10" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165379270.gif" border=0 width="121" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                        <A HREF="#11" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165465270.gif" border=0 width="101" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                       <A HREF="#12" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165570270.gif" border=0 width="112" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#13" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165690270.gif" border=0 width="144" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                  <A HREF="#14" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="1657c9270.gif" border=0 width="201" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#15" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165881270.gif" border=0 width="129" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                      <A HREF="#16" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="16597b270.gif" border=0 width="123" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                 <A HREF="#17" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165a79270.gif" border=0 width="121" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#18" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165b97270.gif" border=0 width="151" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>                <A HREF="#19" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165c84290.gif" border=0 width="132" height="41" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A>               <A HREF="#20" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165d87270.gif" border=0 width="135" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#21" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165e87270.gif" border=0 width="135" height="39" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> <div> <A HREF="#22" TITLE="Teoremas fundamentales del cálculo"><U><IMG SRC="165f29370.gif" border=0 width="553" height="55" ALT="MathType 5.0 Equation" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></U></A></div> </tD> </tR> </TABLE></div> <div> <B> </B></div> <DIV ALIGN="LEFT"></DIV> <div> <B>S o l u c i o n e s </B></div> <bR> <div>  <A NAME="1"><IMG BORDER="0" 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